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Learning from Observations

Chapter 18Section 1 – 3

Outline

• Learning agents• Inductive learning• Decision tree learning

The idea behind learning

• Percepts should be used not only for acting, but also for improving the agent's ability to act in the future.

Learning

• takes place as the agent observes its interactions with the world and its own decision-making processes

• can range from trivial memorization of experience, as exhibited by the wumnpus-world agent, to the creation of entire scientific theories, as exhibited by Albert Einstein

Learning

• Learning is essential for unknown environments,– i.e., when designer lacks omniscience

• Learning is useful as a system construction method,– i.e., expose the agent to reality rather than trying to

write it down

• Learning modifies the agent's decision mechanisms to improve performance

Learning agents

performance element: decides what actions to take learning element: modifies the performance element so that it makes better decisions.

Learning element• Design of a learning element is affected by

– Which components of the performance element are to be learned (chapter 2)

– What feedback is available to learn these components– What representation is used for the components

• Type of feedback:– Supervised learning: correct answers for each

example– Unsupervised learning: correct answers not given– Reinforcement learning: occasional rewards

Learning types• Supervised learning:

a situation in which sample (input, output) pairs of the function to be learned can be perceived or are given

– You can think it as if there is a kind teacher– Eg. an agent training to become a taxi driver. Every

time the instructor shouts "Brake!" the agent can learn a condition-action rule for when to brake

• Reinforcement learning: in the case of the agent acts on its environment, it receives

some evaluation of its action (reinforcement), but is not told of which action is the correct one to achieve its goal

Inductive learning• Simplest form: learn a function from examples

f is the target function

An example is a pair (x, f(x))

Problem: find a hypothesis hsuch that h ≈ fgiven a training set of examples

(This is a highly simplified model of real learning:– Ignores prior knowledge– Assumes examples are given)

–

•

•

Inductive learning method• Construct/adjust h to agree with f on training set• (h is consistent if it agrees with f on all examples)• E.g., curve fitting(曲线拟合 ):

••

Inductive learning method• Construct/adjust h to agree with f on training set• (h is consistent if it agrees with f on all examples)• E.g., curve fitting:

••

Not consistent!

(1) linear hypothesis. F(x)=ax+b


••

Not consistent!

(2) F(x)=ax2+bx+c


••

(c)


• (d)


• (c),(d),(e) consistent, which one should be chosen?• Ockham’s razor: prefer the simplest hypothesis consistent with

data• degree- 1 polynomial is simpler than a degree- 12 polynomial.

•

(e)

Learning decision trees

• Decision tree induction is one of the simplest, and yet most successful forms of learning algorithm.

• A decision tree takes as input an object or situation described by a set of attributes and returns a "decision”-the predicted output value for the input.

Section 18.3. Learning Decision Trees

Learning decision trees

• The input attributes can be discrete or continuous.

• learning a discrete-valued function is called classification learning分类学习 ;

• learning a continuous function is called regression回归 .


How to construct decision trees

• A decision tree reaches its decision by performing a sequence of tests.

• Each internal node in the tree corresponds to a test of the value of one of the properties

• the branches from the node are labeled with the possible values of the test

• Each leaf node in the tree specifies the value to be returned if that leaf is reached.

Learning decision treesProblem: decide whether to wait for a table at a restaurant,

based on the following attributes:1. Alternate: is there an alternative restaurant nearby?2. Bar: is there a comfortable bar area to wait in?3. Fri/Sat: is today Friday or Saturday?4. Hungry: are we hungry?5. Patrons: number of people in the restaurant (None, Some, Full)6. Price: price range ($, $$, $$$)7. Raining: is it raining outside?8. Reservation: have we made a reservation?9. Type: kind of restaurant (French, Italian, Thai, Burger)10. WaitEstimate: estimated waiting time (0-10, 10-30, 30-60, >60)


Attribute-based representations• Examples described by attribute values (Boolean, discrete, continuous)• E.g., situations where I will/won't wait for a table:

• Classification of examples is positive (T) or negative (F)

•

training set• Positive examples are the ones in which the goal

is true• Negative examples are the ones in which it is

false • The complete set of examples is called the

training set.• Q: In previous example,training set={x1,x2,

……x12}– which are Positive examples ?– which are Negative examples?

Decision trees• One possible representation for hypotheses• E.g., here is the “true” tree for deciding whether to wait:

Expressiveness• Logically speaking, any particular decision

tree hypothesis for the Will Wait goal predicate can be seen as an assertion of the form

• Pi(s) is a conjunction of tests corresponding to a path from the root of the tree to a leaf with a positive outcome.

Expressiveness

• P1(s):Patrons=Some• P2(s):Patrons=Full WaitEstimate=30-60 Alternate=No∧ ∧

Reservation=No Bar=Yes∧ ∧• …

Expressiveness• Decision trees can express any function of the input attributes.• E.g., for Boolean functions, truth table row → path to leaf:

• Trivially, there is a consistent decision tree for any training set with one path to leaf for each example (unless f nondeterministic in x) but it probably won't generalize to new examples

• Prefer to find more compact decision trees

Hypothesis spacesHow many distinct decision trees with n Boolean attributes?= number of Boolean functions= number of distinct truth tables with 2n rows

= 22n ("answer" column of the table as a 2n-bit number that defines the function).

• E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees

Hypothesis spacesHow many distinct decision trees with n Boolean attributes?= number of Boolean functions= number of distinct truth tables with 2n rows = 22n

• E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees

How many purely conjunctive hypotheses (e.g., Hungry Rain)?• Each attribute can be in (positive), in (negative), or out

3n distinct conjunctive hypotheses• More expressive hypothesis space

– increases chance that target function can be expressed– increases number of hypotheses consistent with training set

may get worse predictions

Decision tree learning

• Aim: find a small tree consistent with the training examples– Smaller tree means less tests, quicker decision

• Idea: (recursively) choose "most important" attribute as root of (sub)tree

– "most important" attribute is the one that makes the most difference to the classification of an example

Decision tree learning• Aim: find a small tree consistent with the training examples• Idea: (recursively) choose "most significant" attribute as root of

(sub)tree

Choosing an attribute• Idea: a good attribute splits the examples into subsets

that are (ideally) "all positive" or "all negative"

• Patrons? is a better choice

•

Using information theory• To implement Choose-Attribute in the DTL

algorithm

• Information Content (Entropy 熵 ): the information content I of the actual

answer is given by I(P(v1), … , P(vn)) = Σi=1 -P(vi) log2 P(vi)

the possible answers vi have probabilities P(vi),

Using information theory

• For a training set containing p positive examples and n negative examples:

• If the coin is loaded to give 99% heads, we get I (1/100,99/100) = 0.08 bits, and as the

• probability of heads goes to 1, the information of the actual answer goes to 0.

npn

npn

npp

npp

npn

nppI

22 loglog),(

Information gain• A chosen attribute A divides the training set E into

subsets E1, … , Ev according to their values for A, where A has v distinct values.

• Information Gain (IG) or reduction in entropy from the attribute test:

• Choose the attribute with the largest IG

v

i ii

i

ii

iii

npn

nppI

npnpAremainder

1

),()(

)(),()( Aremaindernpn

nppIAIG

Information gainFor the training set, p = n = 6, I(6/12, 6/12) = 1 bit

Consider the attributes Patrons and Type (and others too):

Patrons has the highest IG of all attributes and so is chosen by the DTL algorithm as the root

bits 0)]42,

42(

124)

42,

42(

124)

21,

21(

122)

21,

21(

122[1)(

bits 0541.)]64,

62(

126)0,1(

124)1,0(

122[1)(

IIIITypeIG

IIIPatronsIG

Example contd.• Decision tree learned from the 12 examples:

• Substantially simpler than “true” tree---a more complex hypothesis isn’t justified by small amount of data

Performance measurement• How do we know that h ≈ f ?

1. Use theorems of computational/statistical learning theory2. Try h on a new test set of examples

(use same distribution over example space as training set)

Learning curve = % correct on test set as a function of training set size

Summary• Learning needed for unknown environments,

lazy designers• Learning agent = performance element +

learning element• For supervised learning, the aim is to find a

simple hypothesis approximately consistent with training examples

• Decision tree learning using information gain • Learning performance = prediction accuracy

measured on test set

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